FA-94956 / Warehouse slotting and bin packing / Open access

Carton selection: carton dims not normalized · case 01

Items that fit a carton lying on their side are reported as needing a larger carton.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Carton inner dimensions are compared in catalogue order while item dims are sorted.

VERIFIED REPAIR

Sort both the padded item dims and the carton inner dims before comparing.

Unsuccessful approach: Leaving the item dims unsorted while carton dims are sorted still depends on catalogue orientation.

Case contract

Item dims [a,b,c], weight kg, sioc flag (ships in own container). cartons [[id, L, W, H, max_kg, cost]]. SIOC items return "SIOC". Otherwise add 1 unit of dunnage per side (2 per dimension); the item fits a carton if the sorted padded dims are each <= the sorted inner dims (any orientation) and kg <= max_kg. Choose the smallest inner volume, then cost, then id. None -> "NO_FIT".

Why this case matters

Cartonization picks the shipping box, which drives material cost and dimensional weight.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(dims, kg, sioc, cartons):
    if sioc:
        return 'SIOC'
    need = sorted(d + 2 for d in dims)
    best = None
    for cid, L, W, H, max_kg, cost in cartons:
        inner = [L, W, H]
        if any(n > c for n, c in zip(need, inner)):
            continue
        if kg > max_kg:
            continue
        key = (L * W * H, cost, cid)
        if best is None or key < best[0]:
            best = (key, cid)
    return best[1] if best else 'NO_FIT'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 6', [[13, 6, 9], 19, False, [['C0', 16, 6, 30, 5, 55], ['C1', 6, 12, 6, 5, 70], ['C2', 6, 8, 12, 20, 90], ['C3', 10, 20, 6, 20, 70], ['C4', 24, 8, 30, 10, 70]]], 'NO_FIT']], [['generated mix 18', [[10, 14, 4], 4.5, False, [['C0', 32, 16, 20, 10, 55], ['C1', 32, 6, 8, 30, 90], ['C2', 16, 6, 6, 20, 40], ['C3', 6, 8, 30, 5, 55], ['C4', 10, 6, 20, 20, 40], ['C5', 32, 20, 6, 20, 90]]], 'C5'], ['generated mix 13', [[5, 2, 14], 5, False, [['C0', 20, 20, 6, 5, 55], ['C1', 32, 16, 8, 20, 90]]], 'C0'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['generated mix 7', [[7, 9, 14], 5, True, [['C0', 16, 16, 4, 20, 55], ['C1', 20, 16, 8, 10, 70], ['C2', 24, 6, 4, 5, 40], ['C3', 10, 8, 30, 10, 90], ['C4', 20, 8, 30, 5, 90], ['C5', 24, 12, 12, 10, 90]]], 'SIOC'], ['generated mix 16', [[6, 4, 3], 19, False, [['C0', 12, 16, 4, 5, 40], ['C1', 32, 16, 4, 10, 90], ['C2', 20, 16, 20, 10, 70], ['C3', 20, 12, 8, 10, 90]]], 'NO_FIT']], [['generated mix 34', [[2, 2, 10], 5, False, [['C0', 6, 6, 4, 20, 55], ['C1', 12, 20, 4, 30, 90]]], 'C1'], ['generated mix 26', [[14, 4, 3], 19, False, [['C0', 32, 12, 8, 10, 70], ['C1', 6, 8, 4, 10, 55], ['C2', 20, 20, 8, 5, 55], ['C3', 12, 6, 12, 20, 55], ['C4', 16, 8, 20, 10, 40], ['C5', 6, 6, 20, 20, 40]]], 'C5'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 18', [[10, 14, 4], 4.5, False, [['C0', 32, 16, 20, 10, 55], ['C1', 32, 6, 8, 30, 90], ['C2', 16, 6, 6, 20, 40], ['C3', 6, 8, 30, 5, 55], ['C4', 10, 6, 20, 20, 40], ['C5', 32, 20, 6, 20, 90]]], 'C5'], ['generated mix 27', [[10, 11, 6], 10, False, [['C0', 20, 20, 8, 30, 90], ['C1', 24, 20, 20, 5, 90], ['C2', 32, 16, 4, 5, 55], ['C3', 10, 16, 30, 5, 55], ['C4', 10, 6, 4, 10, 90], ['C5', 16, 20, 30, 5, 70]]], 'C0']], [['generated mix 55', [[14, 7, 5], 9.5, False, [['C0', 16, 8, 6, 30, 55], ['C1', 12, 16, 4, 30, 90], ['C2', 32, 8, 20, 30, 70]]], 'C2'], ['generated mix 39', [[13, 2, 3], 9.5, False, [['C0', 24, 12, 6, 5, 90], ['C1', 32, 8, 6, 30, 90]]], 'C1'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['generated mix 29', [[2, 4, 9], 9.5, False, [['C0', 32, 20, 6, 10, 40], ['C1', 32, 8, 30, 10, 55]]], 'C0'], ['generated mix 37', [[2, 4, 13], 1, True, [['C0', 32, 12, 6, 30, 55], ['C1', 16, 6, 30, 30, 70], ['C2', 6, 8, 6, 5, 55], ['C3', 32, 16, 30, 10, 40], ['C4', 16, 16, 12, 30, 70], ['C5', 16, 8, 6, 10, 90]]], 'SIOC']], [['generated mix 67', [[13, 6, 8], 9.5, False, [['C0', 12, 12, 8, 30, 40], ['C1', 24, 12, 8, 5, 55], ['C2', 24, 20, 8, 30, 40], ['C3', 6, 8, 12, 10, 55]]], 'C2'], ['generated mix 53', [[13, 7, 9], 1, False, [['C0', 32, 16, 30, 30, 70], ['C1', 24, 12, 12, 20, 70], ['C2', 10, 12, 20, 10, 40], ['C3', 12, 12, 30, 10, 40]]], 'C2'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['generated mix 40', [[5, 12, 11], 9.5, False, [['C0', 20, 20, 20, 5, 40], ['C1', 6, 8, 12, 30, 70], ['C2', 10, 16, 12, 5, 40]]], 'NO_FIT'], ['generated mix 48', [[14, 11, 11], 19, False, [['C0', 20, 16, 4, 5, 40], ['C1', 24, 20, 6, 10, 55], ['C2', 32, 6, 6, 10, 90]]], 'NO_FIT']]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
rotated fit	`L`	`S`	Failed
padding pushes to M	`L`	`M`	Failed
weight at limit	`S`	`S`	Passed
sioc	`SIOC`	`SIOC`	Passed
volume tie by cost	`B`	`B`	Passed
long thin carton	`LONG`	`LONG`	Passed
weight over limit	`M`	`M`	Passed
generated mix 6	`NO_FIT`	`NO_FIT`	Passed

SHA-256 / 7f7027114cdd52d785f1b1a4e2a8c59ea11fbff403515fa86b8412ba20aab897

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(dims, kg, sioc, cartons):
    if sioc:
        return 'SIOC'
    need = [d + 2 for d in dims]
    best = None
    for cid, L, W, H, max_kg, cost in cartons:
        inner = sorted([L, W, H])
        if any(n > c for n, c in zip(need, inner)):
            continue
        if kg > max_kg:
            continue
        key = (L * W * H, cost, cid)
        if best is None or key < best[0]:
            best = (key, cid)
    return best[1] if best else 'NO_FIT'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 6', [[13, 6, 9], 19, False, [['C0', 16, 6, 30, 5, 55], ['C1', 6, 12, 6, 5, 70], ['C2', 6, 8, 12, 20, 90], ['C3', 10, 20, 6, 20, 70], ['C4', 24, 8, 30, 10, 70]]], 'NO_FIT']], [['generated mix 18', [[10, 14, 4], 4.5, False, [['C0', 32, 16, 20, 10, 55], ['C1', 32, 6, 8, 30, 90], ['C2', 16, 6, 6, 20, 40], ['C3', 6, 8, 30, 5, 55], ['C4', 10, 6, 20, 20, 40], ['C5', 32, 20, 6, 20, 90]]], 'C5'], ['generated mix 13', [[5, 2, 14], 5, False, [['C0', 20, 20, 6, 5, 55], ['C1', 32, 16, 8, 20, 90]]], 'C0'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['generated mix 7', [[7, 9, 14], 5, True, [['C0', 16, 16, 4, 20, 55], ['C1', 20, 16, 8, 10, 70], ['C2', 24, 6, 4, 5, 40], ['C3', 10, 8, 30, 10, 90], ['C4', 20, 8, 30, 5, 90], ['C5', 24, 12, 12, 10, 90]]], 'SIOC'], ['generated mix 16', [[6, 4, 3], 19, False, [['C0', 12, 16, 4, 5, 40], ['C1', 32, 16, 4, 10, 90], ['C2', 20, 16, 20, 10, 70], ['C3', 20, 12, 8, 10, 90]]], 'NO_FIT']], [['generated mix 34', [[2, 2, 10], 5, False, [['C0', 6, 6, 4, 20, 55], ['C1', 12, 20, 4, 30, 90]]], 'C1'], ['generated mix 26', [[14, 4, 3], 19, False, [['C0', 32, 12, 8, 10, 70], ['C1', 6, 8, 4, 10, 55], ['C2', 20, 20, 8, 5, 55], ['C3', 12, 6, 12, 20, 55], ['C4', 16, 8, 20, 10, 40], ['C5', 6, 6, 20, 20, 40]]], 'C5'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 18', [[10, 14, 4], 4.5, False, [['C0', 32, 16, 20, 10, 55], ['C1', 32, 6, 8, 30, 90], ['C2', 16, 6, 6, 20, 40], ['C3', 6, 8, 30, 5, 55], ['C4', 10, 6, 20, 20, 40], ['C5', 32, 20, 6, 20, 90]]], 'C5'], ['generated mix 27', [[10, 11, 6], 10, False, [['C0', 20, 20, 8, 30, 90], ['C1', 24, 20, 20, 5, 90], ['C2', 32, 16, 4, 5, 55], ['C3', 10, 16, 30, 5, 55], ['C4', 10, 6, 4, 10, 90], ['C5', 16, 20, 30, 5, 70]]], 'C0']], [['generated mix 55', [[14, 7, 5], 9.5, False, [['C0', 16, 8, 6, 30, 55], ['C1', 12, 16, 4, 30, 90], ['C2', 32, 8, 20, 30, 70]]], 'C2'], ['generated mix 39', [[13, 2, 3], 9.5, False, [['C0', 24, 12, 6, 5, 90], ['C1', 32, 8, 6, 30, 90]]], 'C1'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['generated mix 29', [[2, 4, 9], 9.5, False, [['C0', 32, 20, 6, 10, 40], ['C1', 32, 8, 30, 10, 55]]], 'C0'], ['generated mix 37', [[2, 4, 13], 1, True, [['C0', 32, 12, 6, 30, 55], ['C1', 16, 6, 30, 30, 70], ['C2', 6, 8, 6, 5, 55], ['C3', 32, 16, 30, 10, 40], ['C4', 16, 16, 12, 30, 70], ['C5', 16, 8, 6, 10, 90]]], 'SIOC']], [['generated mix 67', [[13, 6, 8], 9.5, False, [['C0', 12, 12, 8, 30, 40], ['C1', 24, 12, 8, 5, 55], ['C2', 24, 20, 8, 30, 40], ['C3', 6, 8, 12, 10, 55]]], 'C2'], ['generated mix 53', [[13, 7, 9], 1, False, [['C0', 32, 16, 30, 30, 70], ['C1', 24, 12, 12, 20, 70], ['C2', 10, 12, 20, 10, 40], ['C3', 12, 12, 30, 10, 40]]], 'C2'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['generated mix 40', [[5, 12, 11], 9.5, False, [['C0', 20, 20, 20, 5, 40], ['C1', 6, 8, 12, 30, 70], ['C2', 10, 16, 12, 5, 40]]], 'NO_FIT'], ['generated mix 48', [[14, 11, 11], 19, False, [['C0', 20, 16, 4, 5, 40], ['C1', 24, 20, 6, 10, 55], ['C2', 32, 6, 6, 10, 90]]], 'NO_FIT']]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
rotated fit	`M`	`S`	Failed
padding pushes to M	`L`	`M`	Failed
weight at limit	`S`	`S`	Passed
sioc	`SIOC`	`SIOC`	Passed
volume tie by cost	`B`	`B`	Passed
long thin carton	`LONG`	`LONG`	Passed
weight over limit	`M`	`M`	Passed
generated mix 6	`NO_FIT`	`NO_FIT`	Passed

SHA-256 / 35bb61a220098eb04c7ac77ea8f239b416d149ba8b2277c685808286c438769a

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(dims, kg, sioc, cartons):
    if sioc:
        return 'SIOC'
    need = sorted(d + 2 for d in dims)
    best = None
    for cid, L, W, H, max_kg, cost in cartons:
        inner = sorted([L, W, H])
        if any(n > c for n, c in zip(need, inner)):
            continue
        if kg > max_kg:
            continue
        key = (L * W * H, cost, cid)
        if best is None or key < best[0]:
            best = (key, cid)
    return best[1] if best else 'NO_FIT'
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 6', [[13, 6, 9], 19, False, [['C0', 16, 6, 30, 5, 55], ['C1', 6, 12, 6, 5, 70], ['C2', 6, 8, 12, 20, 90], ['C3', 10, 20, 6, 20, 70], ['C4', 24, 8, 30, 10, 70]]], 'NO_FIT']], [['generated mix 18', [[10, 14, 4], 4.5, False, [['C0', 32, 16, 20, 10, 55], ['C1', 32, 6, 8, 30, 90], ['C2', 16, 6, 6, 20, 40], ['C3', 6, 8, 30, 5, 55], ['C4', 10, 6, 20, 20, 40], ['C5', 32, 20, 6, 20, 90]]], 'C5'], ['generated mix 13', [[5, 2, 14], 5, False, [['C0', 20, 20, 6, 5, 55], ['C1', 32, 16, 8, 20, 90]]], 'C0'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['generated mix 7', [[7, 9, 14], 5, True, [['C0', 16, 16, 4, 20, 55], ['C1', 20, 16, 8, 10, 70], ['C2', 24, 6, 4, 5, 40], ['C3', 10, 8, 30, 10, 90], ['C4', 20, 8, 30, 5, 90], ['C5', 24, 12, 12, 10, 90]]], 'SIOC'], ['generated mix 16', [[6, 4, 3], 19, False, [['C0', 12, 16, 4, 5, 40], ['C1', 32, 16, 4, 10, 90], ['C2', 20, 16, 20, 10, 70], ['C3', 20, 12, 8, 10, 90]]], 'NO_FIT']], [['generated mix 34', [[2, 2, 10], 5, False, [['C0', 6, 6, 4, 20, 55], ['C1', 12, 20, 4, 30, 90]]], 'C1'], ['generated mix 26', [[14, 4, 3], 19, False, [['C0', 32, 12, 8, 10, 70], ['C1', 6, 8, 4, 10, 55], ['C2', 20, 20, 8, 5, 55], ['C3', 12, 6, 12, 20, 55], ['C4', 16, 8, 20, 10, 40], ['C5', 6, 6, 20, 20, 40]]], 'C5'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['long thin carton', [[3, 3, 3], 1, False, [['LONG', 40, 6, 6, 30, 50], ['CUBE', 12, 12, 12, 30, 60]]], 'LONG'], ['padding pushes to M', [[11, 3, 3], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['generated mix 18', [[10, 14, 4], 4.5, False, [['C0', 32, 16, 20, 10, 55], ['C1', 32, 6, 8, 30, 90], ['C2', 16, 6, 6, 20, 40], ['C3', 6, 8, 30, 5, 55], ['C4', 10, 6, 20, 20, 40], ['C5', 32, 20, 6, 20, 90]]], 'C5'], ['generated mix 27', [[10, 11, 6], 10, False, [['C0', 20, 20, 8, 30, 90], ['C1', 24, 20, 20, 5, 90], ['C2', 32, 16, 4, 5, 55], ['C3', 10, 16, 30, 5, 55], ['C4', 10, 6, 4, 10, 90], ['C5', 16, 20, 30, 5, 70]]], 'C0']], [['generated mix 55', [[14, 7, 5], 9.5, False, [['C0', 16, 8, 6, 30, 55], ['C1', 12, 16, 4, 30, 90], ['C2', 32, 8, 20, 30, 70]]], 'C2'], ['generated mix 39', [[13, 2, 3], 9.5, False, [['C0', 24, 12, 6, 5, 90], ['C1', 32, 8, 6, 30, 90]]], 'C1'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['weight at limit', [[3, 3, 3], 10, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['sioc', [[3, 3, 3], 1, True, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'SIOC'], ['volume tie by cost', [[3, 3, 3], 1, False, [['A', 10, 10, 10, 9, 60], ['B', 20, 10, 5, 9, 55]]], 'B'], ['generated mix 29', [[2, 4, 9], 9.5, False, [['C0', 32, 20, 6, 10, 40], ['C1', 32, 8, 30, 10, 55]]], 'C0'], ['generated mix 37', [[2, 4, 13], 1, True, [['C0', 32, 12, 6, 30, 55], ['C1', 16, 6, 30, 30, 70], ['C2', 6, 8, 6, 5, 55], ['C3', 32, 16, 30, 10, 40], ['C4', 16, 16, 12, 30, 70], ['C5', 16, 8, 6, 10, 90]]], 'SIOC']], [['generated mix 67', [[13, 6, 8], 9.5, False, [['C0', 12, 12, 8, 30, 40], ['C1', 24, 12, 8, 5, 55], ['C2', 24, 20, 8, 30, 40], ['C3', 6, 8, 12, 10, 55]]], 'C2'], ['generated mix 53', [[13, 7, 9], 1, False, [['C0', 32, 16, 30, 30, 70], ['C1', 24, 12, 12, 20, 70], ['C2', 10, 12, 20, 10, 40], ['C3', 12, 12, 30, 10, 40]]], 'C2'], ['weight over limit', [[3, 3, 3], 10.5, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'M'], ['no fit', [[40, 3, 3], 1, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'NO_FIT'], ['cheap but bulky', [[3, 3, 3], 1, False, [['BIG', 30, 30, 30, 30, 40], ['SMALL', 10, 10, 10, 30, 60]]], 'SMALL'], ['rotated fit', [[4, 10, 8], 3, False, [['S', 12, 10, 6, 10, 50], ['M', 16, 12, 10, 20, 70], ['L', 24, 18, 14, 30, 95]]], 'S'], ['generated mix 40', [[5, 12, 11], 9.5, False, [['C0', 20, 20, 20, 5, 40], ['C1', 6, 8, 12, 30, 70], ['C2', 10, 16, 12, 5, 40]]], 'NO_FIT'], ['generated mix 48', [[14, 11, 11], 19, False, [['C0', 20, 16, 4, 5, 40], ['C1', 24, 20, 6, 10, 55], ['C2', 32, 6, 6, 10, 90]]], 'NO_FIT']]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
rotated fit	`S`	`S`	Passed
padding pushes to M	`M`	`M`	Passed
weight at limit	`S`	`S`	Passed
sioc	`SIOC`	`SIOC`	Passed
volume tie by cost	`B`	`B`	Passed
long thin carton	`LONG`	`LONG`	Passed
weight over limit	`M`	`M`	Passed
generated mix 6	`NO_FIT`	`NO_FIT`	Passed

SHA-256 / d8937a1f4457e19927145aa1613ace7df82631b4903649b5bc9c3145ef9a9ef8

Verification & scope

Stipulated fit rule with uniform dunnage; no void-fill or multi-item cartonization. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:52:09.235222+00:00.

Case digest / d8e74bfc90d50595355b76707308196c0879a46218bcf4ffde4c11f4d76ffcfc